WASHINGTON — Lawyers for Twitter users blocked by President Trump after they criticized or mocked him are asking him to reverse the moves, arguing that the Constitution bars him from blocking people on the social media service.

The request raises novel legal issues stemming from Mr. Trump’s use of his Twitter account, @realDonaldTrump, to make statements about public policy. In a letter sent to Mr. Trump on Tuesday, lawyers for several users he has blocked argued that his account was a “public forum” from which the government may not constitutionally exclude people because it disagrees with views they have expressed.

“This Twitter account operates as a ‘designated public forum’ for First Amendment purposes, and accordingly the viewpoint-based blocking of our clients is unconstitutional,” the letter said. “We ask that you unblock them and any others who have been blocked for similar reasons.”

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Jameel Jaffer, the executive director of the Knight First Amendment Institute at Columbia University, which is representing the blocked Twitter users.CreditBrendan Smialowski/Agence France-Presse — Getty Images

The letter implies that if the Trump administration does not comply, a lawsuit may follow. The blocked Twitter users are represented by the Knight First Amendment Institute at Columbia University, whose executive director, Jameel Jaffer, said in a statement that Mr. Trump did not have a right to exclude his critics from engaging with his posts.

“Though the architects of the Constitution surely didn’t contemplate presidential Twitter accounts, they understood that the president must not be allowed to banish views from public discourse simply because he finds them objectionable,” Mr. Jaffer said. “Having opened this forum to all comers, the president can’t exclude people from it merely because he dislikes what they’re saying.”

The letter said that Mr. Trump’s blocking of users on Twitter suppressed their free-expression rights in several ways. Users of blocked accounts cannot follow Mr. Trump and they have difficulty viewing his posts, finding them through Twitter’s search function, learning which accounts follow the president and participating in comment-thread discussions about his tweets, it said.

One of the Twitter users the letter said Mr. Trump had blocked is Holly O’Reilly, whose account is @AynRandPaulRyan.

On May 28, Mr. Trump posted a message about the British prime minister being angry that information about a suspect in the Manchester terrorist attack that Britain had given to the United States had been leaked. Ms. O’Reilly, who identified herself as an organizer of the June 3 March for Truth rally, posted a series of responses to Mr. Trump’s tweet that appeared beneath it, mocking him and promoting the protest, which was held in several locations.

“YOU ARE THE LEAKER, you bloody idiot. God, you’re embarrassing,” her first message said. She followed it up with several others, including a moving GIF image of Pope Francis glancing at Mr. Trump with an uncomfortable expression, above which she wrote, “This is pretty much how the whole world sees you.”

In the letter, Ms. O’Reilly’s lawyers wrote: “Of course, it is easy to understand why you and your advisers might have found our clients’ posts to be disagreeable. Even if the posts were scornful and acerbic, however, they were protected by the First Amendment.”

They added: “The protection of speech critical of government officials is perhaps the core concern of the First Amendment, because the freedom of individuals to engage in this kind of speech is crucial to self-government.”

The letter was copied to the White House counsel, Donald F. McGahn II; the White House press secretary, Sean Spicer; and the White House director of social media, Dan Scavino Jr.